Edward married Dorothy Rogers, daughter of John Rogers of Pickhill, Denbighshire.

They had 7 children:

John, who married Mary, by whom he had a son Richard

Roger Puleston of Willingdon, who married Akice and was buried at Worthenbury on 7 March 1670 - his will was dated 20 September 1669. They had 5 children (all baptised at Worthenbury) - Roger (1634/5), Susan (December 1637 - in 1661, she married Peter Woodward of Chester), Elizabeth (1641 - on 28 February 1662, she was married at Worthenbury to William Ffarrell of Charlton), Thomas (September 1646) and John (18 June 1652 - he married Jane, moved to the Wern and founded that branch of the Pulestons. He was buried at Worthenbury on 1 October 1693. His will was dated 14 July 1692)

The National Library of Wales, Aberystwyth holds in the Harold T Elwes collection of manuscripts a document (no. 797) in Latin and English dated 8 January 1641/2 between (1) John Llewelyn of Bangor, co. Flint, yeoman and (2) Edward Puleston of Pickhill, co. Denbigh, gentleman. It is described in the index as a bond for the performance of covenants of the same date.